Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } - 2 x + 6 y - 15 = 0$$
A) no; the graph is the point $( 1 , - 3 )$
B) no; the graph is nonexistent
C) no; the graph is the point $( - 1,3 )$
D) yes

Question

Quizplus · Accepted Answer

The given equation is of the form $x^2 + y^2 - 2x + 6y - 15 = 0$, which can be rewritten in the standard form of a circle's equation by completing the squares for $x$ and $y$. This shows it represents a circle, not a point or a nonexistent graph.

Decide Whether or Not the Equation Has a Circle as Its